Method for manufacturing a quartz crystal resonator, quartz crystal unit and quartz crystal oscillator

ABSTRACT

A method for manufacturing a quartz crystal unit comprises the steps of forming a quartz crystal tuning fork resonator having a quartz crystal tuning fork shape, forming at least one groove in at least one of opposite main surfaces of each of first and second quartz crystal tuning fork tines so that a spaced-apart distance between the first and second quartz crystal tuning fork tines is greater than or equal to a width of the at least one groove, determining the dimension of each of the quartz crystal tuning fork shape and the at least one groove so that a capacitance ratio r 1  of a fundamental mode of vibration of the quartz crystal tuning fork resonator is less than a capacitance ratio r 2  of a second overtone mode of vibration thereof, mounting the quartz crystal tuning fork resonator on a mounting portion of a case, and connecting a lid to the case to cover an open end of the case.

CROSS REFERENCE TO RELATED APPLICATIONS

This is a division of application Ser. No. 12/009,283 filed Jan. 17,2008 and now Pat. No. 7,779,530, which is a continuation of applicationSer. No. 11/821,753 filed Jun. 25, 2007 and now U.S. Pat. No. 7,564,326, which is a continuation of application Ser. No. 11/398,876 filedApr. 6, 2006 and now abandoned, which is a division of application Ser.No. 10/749,182 filed Dec. 30, 2003 and now U.S. Pat. No. 7,071,794,which is a continuation-in-part of application Ser. No. 10/378,719 filedMar. 4, 2003 and now abandoned, all of which are hereby incorporated byreference.

FIELD OF THE INVENTION

The present invention relates to an electronic apparatus comprising adisplay portion and a quartz crystal oscillator at least.

BACKGROUND OF THE INVENTION

There are many electronic apparatus comprising a display portion and aquartz crystal oscillator at least. For example, cellular phones,wristwatches, facsimiles and pagers comprising a quartz crystaloscillator are well known. Recently, because of high stability forfrequency, miniaturization and the light weight nature of theseelectronic apparatus, the need for an electronic apparatus comprising asmaller quartz crystal oscillator with a high frequency stability hasarisen. For example, the quartz crystal oscillator with a quartz crystaltuning fork resonator, which is capable of vibrating in a flexural mode,is widely used as a time standard in an electronic apparatus such as thecellular phones, the wristwatches, the facsimiles and the pagers.Similar to this, the same need has also arisen for an electronicapparatus comprising a length-extensional mode quartz crystal resonatorwith a frequency of 1 MHz to 10 MHz to decrease an electric currentconsumption of the electronic apparatus.

Heretofore, however, it has been impossible to obtain an electronicapparatus comprising a smaller quartz crystal oscillator with aconventional miniaturized quartz crystal tuning fork resonator, capableof vibrating in a flexural mode, and having a high frequency stability,a small series resistance and a high quality factor. When miniaturized,the conventional quartz crystal tuning fork resonator, capable ofvibrating in a flexural mode, as shown in FIG. 12 (which has electrodeson the obverse faces 203, 207, reverse faces 204, 208 and the four sides205, 206, 209, 210 of each tuning fork tine, as also shown in FIG. 13—across-sectional view of tuning fork tines of FIG. 12), it has a smallerelectromechanical transformation efficiency because the resonator shapeand the electrode construction provide a small electric field (i.e. Exbecomes small), as a result of which the resonator has a low frequencystability, a large series resistance and a reduced quality factor. InFIG. 12, a conventional tuning fork resonator 200 is shown with tines201, 202 and a base 230.

Moreover, for example, Japanese Patent Nos. P56-65517 and P2000-223992Aand International Patent No. WO 00/44092 were published and teachgrooves and electrodes constructed at tuning fork tines of a flexuralmode, tuning fork, quartz crystal resonator. However, they teach nothingabout a quartz crystal oscillator of the present invention having novelshape, novel electrode construction and figure of merit M for a quartzcrystal tuning fork resonator, capable of vibrating in a flexural modeand about a relationship of an amplification circuit and a feedbackcircuit which construct a quartz crystal oscillating circuit.

Additionally, for example, there has been a big problem in theconventional oscillator with the conventional quartz crystal tuning forkresonator, such that a fundamental mode vibration of the resonator jumpsto a second overtone mode vibration by shock or vibration.

Similarly, however, it has been impossible to obtain an electronicapparatus comprising a smaller quartz crystal oscillator with aconventional length-extensional mode quartz crystal resonator, capableof vibrating in a length-extensional mode, and having a frequency of 1MHz to 10 MHz, a small series resistance and a high quality factor. Asan example of a length-extensional mode quartz crystal resonator of theprior art, the length-extensional mode resonator comprising avibrational portion, connecting portions and supporting portions, whichis formed from a Z plate perpendicular to z axis, is well known, andthis resonator is formed integrally by a chemical etching process. Also,electrodes are disposed opposite each other on sides of the vibrationalportion formed by the chemical etching process so that the electrodesdisposed opposite each other are of opposite electrical polarity.

Also, a cutting angle of the conventional length-extensional mode quartzcrystal resonator is generally within a range of ZYw (0° to +5°),according to an IEEE notation. In detail, the connecting portions areconnected opposite each other at both end portions of a width of thevibrational portion and at a central portion of the length directionthereof. Namely, the direction of the connecting portions constructedopposite each other corresponds to the direction of the electric field.

When an alternating current (AC) voltage is applied between theelectrodes, an electric field occurs alternately in the width direction,as a result, the resonator is capable of vibrating in the lengthdirection, but the electric field of between the electrodes becomes verysmall because quartz crystal is an anisotropic material and the sides ofthe vibrational portion have a complicated shape formed by the chemicaletching process. Namely, the resonator has small electromechanicaltransformation efficiency because the resonator's shape and theelectrode construction provide a small electric field, consequently, theresonator has a low frequency stability, a large series resistance and areduced quality factor when it has the frequency of 1 MHz to 10 MHz.

It is, therefore, a general object of the present invention to provideembodiments of an electronic apparatus and a quartz crystal oscillator,which constructs an electronic apparatus of the present invention,comprising a quartz crystal oscillating circuit with a flexural mode,quartz crystal tuning fork resonator, capable of vibrating in afundamental mode, and having a high frequency stability, a small seriesresistance and a high quality factor, or embodiments of a quartz crystaloscillator, which also constructs an electronic apparatus of the presentinvention, comprising a quartz crystal oscillating circuit with alength-extensional mode quartz crystal resonator having a frequency of 1MHz to 10 MHz, a small series resistance and a high quality factor,which overcome or at least mitigate one or more of the above problems.

SUMMARY OF THE INVENTION

The present invention relates to an electronic apparatus comprising adisplay portion and a quartz crystal oscillator at least, and the quartzcrystal oscillator comprises a quartz crystal oscillating circuit havingan amplification circuit and a feedback circuit, and in particular,relates to a quartz crystal oscillator having a flexural mode, quartzcrystal tuning fork resonator capable of vibrating in a fundamental modeand having an output signal of a high frequency stability for thefundamental mode vibration of the resonator, and also to a quartzcrystal oscillator having a suppressed second overtone mode vibration ofthe flexural mode, quartz crystal tuning fork resonator, in addition,relates to a quartz crystal oscillator comprising a length-extensionalmode quartz crystal resonator. The quartz crystal oscillators are,therefore, available for the electronic apparatus requiring miniaturizedand low priced quartz crystal oscillators with high time accuracy andshock proof.

It is an object of the present invention to provide an electronicapparatus comprising a quartz crystal oscillator with a miniature quartzcrystal tuning fork resonator, capable of vibrating in a flexural mode,and having a high frequency stability, a small series resistance R₁ anda high quality factor Q₁, whose nominal frequency for a fundamental modevibration is within a range of 10 kHz to 200 kHz.

It is an another object of the present invention to provide anelectronic apparatus comprising a quartz crystal oscillator with aflexural mode, quartz crystal tuning fork resonator, capable ofvibrating in a fundamental mode, and having a high frequency stabilitywhich gives a high time accuracy.

It is a further object of the present invention to provide an electronicapparatus comprising a quartz crystal oscillator with alength-extensional mode quartz crystal resonator.

According to one aspect of the present invention, there is provided anelectronic apparatus comprising a display portion and a quartz crystaloscillator at least, and said electronic apparatus having one quartzcrystal oscillator, said one quartz crystal oscillator comprising: aquartz crystal oscillating circuit comprising; an amplification circuitcomprising an amplifier at least and a feedback circuit comprising aquartz crystal resonator and capacitors at least, said quartz crystalresonator being a quartz crystal tuning fork resonator, capable ofvibrating in a flexural mode, and said quartz crystal tuning forkresonator comprising: tuning fork tines each of which has a length, awidth and a thickness and the length greater than the width and thethickness; and a tuning fork base; said tuning fork tines and saidtuning fork base that are formed integrally; and electrodes disposedfacing each other on sides of said tuning fork tines so that theelectrodes disposed facing each other are of opposite electricalpolarity and said tuning fork tines are capable of vibrating in inversephase,

According to a second aspect of the present invention there is providedan electronic apparatus comprising a display portion and a quartzcrystal oscillator at least, and said electronic apparatus comprises atleast one quartz crystal oscillator comprising: an oscillating circuitcomprising; an amplification circuit comprising an amplifier at least,and a feedback circuit comprising a length-extensional mode quartzcrystal resonator which is one of a contour mode quartz crystalresonator.

According to a third aspect of the present invention, there is provideda method for manufacturing an electronic apparatus comprising a displayportion and a quartz crystal oscillator at least, and said electronicapparatus comprising at least one quartz crystal oscillator, said atleast one oscillator comprising: a quartz crystal oscillating circuitcomprising; an amplification circuit comprising an amplifier at least,and a feedback circuit comprising a quartz crystal resonator andcapacitors at least, said quartz crystal resonator being a quartzcrystal tuning fork resonator, capable of vibrating in a flexural mode,said quartz crystal tuning fork resonator comprising the steps of:forming integrally tuning fork tines each of which has a length, a widthand a thickness and the length greater than the width and the thicknessand a tuning fork base; disposing electrodes facing each other on sidesof said tuning fork tines so that the electrodes disposed facing eachother are of opposite electrical polarity and said tuning fork tinesvibrate an in inverse phase; and adjusting resonance frequency of saidquartz crystal tuning fork resonator after mounting it at a mountingportion by conductive adhesives or solder so that a frequency deviationis within a range of −100 PPM to +100 PPM.

According to a fourth aspect of the present invention, there areprovided a quartz crystal resonator, a quartz crystal unit and a quartzcrystal oscillator, each of which has a piezoelectric constant e₁₂ thatis within a range of 0.095 C/m² to 0.19 C/m².

Preferably, said tuning fork resonator is constructed so that figure ofmerit M₁ of a fundamental mode vibration is larger than figure of meritM₂ of a second overtone mode vibration.

Preferably, the quartz crystal oscillator with said tuning forkresonator is constructed so that a ratio of an amplification rate α₁ ofthe fundamental mode vibration and an amplification rate α₂ of thesecond overtone mode vibration of said amplification circuit is largerthan that of a feedback rate β₂ of the second overtone mode vibrationand a feedback rate β₁ of the fundamental mode vibration of saidfeedback circuit, and a product of the amplification rate α₁ and thefeedback rate β₁ of the fundamental mode vibration is larger than 1.

Preferably, the quartz crystal oscillator with said tuning forkresonator is constructed so that a ratio of an absolute value ofnegative resistance, |−RL₁| of the fundamental mode vibration of saidamplification circuit and series resistance R₁ of the fundamental modevibration is larger than that of an absolute value of negativeresistance, |RL₂| of the second overtone mode vibration of saidamplification circuit and series resistance R₂ of the second overtonemode vibration.

Preferably, the length-extensional mode quartz crystal resonatorcomprises a vibrational portion, connecting portions and supportingportions, which are formed integrally by a particle method.

The present invention will be more fully understood by referring to thefollowing detailed specification and claims taken in connection with theappended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a block diagram of an embodiment of an electronic apparatusof the present invention, and illustrating the diagram of a facsimileapparatus;

FIG. 2 shows a diagram of an embodiment of a quartz crystal oscillatingcircuit constructing a quartz crystal oscillator, which constructs anelectronic apparatus of the present invention;

FIG. 3 shows a diagram of the feedback circuit of FIG. 2;

FIG. 4 shows a general view of a flexural mode, quartz crystal tuningfork resonator constructing a quartz crystal oscillator, whichconstructs an electronic apparatus of the first embodiment of thepresent invention;

FIG. 5 shows a D-D′ cross-sectional view of the tuning fork base of FIG.4, and illustrating electrode construction;

FIG. 6 shows a plan view of a quartz crystal tuning fork resonator ofFIG. 4;

FIG. 7 shows a plan view of a flexural mode, quartz crystal tuning forkresonator constructing a quartz crystal oscillator, which constructs anelectronic apparatus of the second embodiment of the present invention;

FIG. 8 a and FIG. 8 b show a top view and a side view of alength-extensional mode quartz crystal resonator constructing a quartzcrystal oscillator, which constructs an electronic apparatus of thethird embodiment of the present invention;

FIG. 9 shows a cross-sectional view of a quartz crystal unitconstructing a quartz crystal oscillator, which constructs an electronicapparatus of the fourth embodiment of the present invention;

FIG. 10 shows a cross-sectional view of a quartz crystal oscillator,which constructs an electronic apparatus of the fifth embodiment of thepresent invention;

FIG. 11 shows a step diagram of a method for manufacturing a quartzcrystal unit constructing a quartz crystal oscillator, which constructsan electronic apparatus of the present invention;

FIG. 12 is a general view of the conventional flexural mode, quartzcrystal tuning fork resonator constructing a quartz crystal oscillatorof the prior art, which constructs the conventional electronicapparatus; and

FIG. 13 is a cross-sectional view of the tuning fork tines of FIG. 12,and illustrating electrode construction.

DETAILED DESCRIPTION

Referring now to the drawings, the embodiments of the present inventionwill be described in more detail.

FIG. 1 shows a block diagram of an embodiment of an electronic apparatusof the present invention, and illustrating the diagram of a facsimileapparatus. As is shown in FIG. 1, the apparatus generally comprises amodem, a phonetic circuit, a timepiece circuit, a printing portion, ataking portion, an operation portion and a display portion. In thisprinciple, perception and scanning of reflection light of lightprojected on manuscript in the taking portion are performed by CCD(Charge Coupled Device), in addition, light and shade of the reflectionlight are transformed into a digital signal, and the signal is modulatedby the modem and is sent to a phone line (Communication line). Also, ina receiving side, a received signal is demodulated by the modem and isprinted on a paper in the print to portion by synchronizing the receivedsignal with a signal of sending side.

As shown in FIG. 1, a quartz crystal resonator is used as a CPU clock ofthe control portion and the printing portion, as a clock of the phoneticcircuit and the modem, and as a time standard of the timepiece. Namely,the resonator constructs a quartz crystal oscillator and an outputsignal of the oscillator is used. For example, it is used as a signal todisplay time at the display portion. In this case, a quartz crystaltuning fork resonator, capable of vibrating in a flexural mode is used,and e.g. as the CPU clock, a contour mode quartz crystal resonator suchas a length-extensional mode quartz crystal resonator or a thicknessshear mode quartz crystal resonator is used. In order to get thefacsimile apparatus of this embodiment which operates normally, anaccuracy output signal of the oscillator is required for the facsimileapparatus, which is one of the electronic apparatus of the presentinvention. Also, a digital display and an analogue display are includedin the display of the present invention.

In this embodiment, though the facsimile apparatus is shown as anexample of an electronic apparatus, the present invention is not limitedto this, namely, the present invention includes all electronicapparatus, each of which comprises a quartz crystal oscillator and adisplay portion at least, for example, cellar phones, telephones, a TVset, cameras, a video set, video cameras, pagers, personal computers,printers, CD players, MD players, electronic musical instruments, carnavigators, car electronics, timepieces, IC cards and so forth.

FIG. 2 shows a diagram of an embodiment of a quartz crystal oscillatingcircuit constructing a quartz crystal oscillator, which constructs anelectronic apparatus of the present invention. The quartz crystaloscillating circuit 1 comprises an amplifier (CMOS Inverter) 2, afeedback resistor 4, a drain resistor 7, capacitors 5, 6 and a flexuralmode, quartz crystal tuning fork resonator 3. Namely, the oscillatingcircuit 1 comprises an amplification circuit 8 having the amplifier 2and the feedback resistor 4, and a feedback circuit 9 having the drainresistor 7, the capacitors 5, 6 and the quartz crystal tuning forkresonator 3. In addition, an output signal of the oscillating circuit 1comprising the quartz crystal tuning fork resonator 3, capable ofvibrating in a fundamental mode, is outputted through a buffer circuit(not shown in FIG. 2).

In detail, an oscillation frequency of the fundamental mode vibration isoutputted through a buffer circuit as an output signal. According to thepresent invention, a nominal frequency of the fundamental mode vibrationof the resonator is within a range of 10 kHz to 200 kHz. Especially,32.768 kHz is an important frequency. In general, the output signal hasan oscillation frequency which is within a range of −100 PPM to +100 PPMto the nominal frequency, e.g. 32.768 kHz. In more detail, the quartzcrystal oscillator in this embodiment comprises a quartz crystaloscillating circuit and a buffer circuit, namely, the quartz crystaloscillating circuit comprises an amplification circuit and a feedbackcircuit, and the amplification circuit comprises an amplifier and afeedback resistor, and the feedback circuit comprises a flexural mode,quartz crystal tuning fork resonator, a drain resistor and capacitors.Also, flexural mode, quartz crystal tuning fork resonators which areused in a quartz crystal oscillator will be described in FIG. 4-FIG. 7in detail. Instead of the flexural mode, quartz crystal tuning forkresonator, a contour mode resonator such as a length-extensional modequartz crystal resonator, a width-extensional mode quartz crystalresonator and a Lame mode quartz crystal resonator or a thickness shearmode quartz crystal resonator may be used.

FIG. 3 shows a diagram of the feedback circuit of FIG. 2. Now, whenangular frequency ω_(i) of the flexural mode, quartz crystal tuning forkresonator 3, capable of vibrating in a flexural mode, a resistance R_(d)of the drain resistor 7, capacitance C_(g), C_(d) of the capacitors 5,6, crystal impedance R_(ei) of the quartz crystal resonator 3, an inputvoltage V₁, and an output voltage V₂ are taken, a feedback rate β_(i) isdefined by β_(i)=|V₂|_(i)/|V₁|_(i), where i shows vibration order, forexample, when i=1 and 2, they are for a fundamental mode vibration and asecond overtone mode vibration.

In addition, load capacitance C_(L) is given byC_(L)=C_(g)C_(d)/(C_(g)+C_(d)), and when C_(g)=C_(d)=C_(gd) andR_(d)>>R_(ei), the feedback rate β_(i) is given by β_(i)=1/(1+kC_(L) ²),where k is expressed by a function of ω_(i), R_(d) and R_(ei). Also,R_(ei) is approximately equal to series resistance R_(i).

Thus, it is easily understood from a relationship of the feedback rateβ_(i) and load capacitance C_(L) that the feedback rate of resonancefrequency for a fundamental mode vibration and an overtone modevibration becomes large, respectively, according to decrease of loadcapacitance C_(L). Therefore, when C_(L) has a small value, anoscillation of the overtone mode occurs very easily, instead of that ofthe fundamental mode. This is the reason why a maximum amplitude of theovertone mode vibration becomes smaller than that of the fundamentalmode vibration, and the oscillation of the overtone mode satisfies anamplitude condition and a phase condition simultaneously which are thecontinuous condition of an oscillation in an oscillating circuit.

As it is also one object of the present invention to provide a quartzcrystal oscillator having a flexural mode, quartz crystal tuning forkresonator, capable of vibrating in a fundamental mode and having a highfrequency stability (high time accuracy) of an output signal, and havingreduced electric current consumption, in this embodiment, loadcapacitance C_(L) is less than 25 pF to reduce electric currentconsumption. To get much reduced electric current consumption, C_(L) ispreferably less than 15 pF because electric current consumption isproportional to C_(L).

In addition, in order to suppress a second overtone mode vibration andto obtain a quartz crystal oscillator having an output signal of anoscillation frequency of a fundamental mode vibration, the quartzcrystal oscillator in this embodiment is constructed so that itsatisfies a relationship of α₁/α₂>β₂/β₁ and α₁β₁>1, where α₁ and α₂ are,respectively, an amplification rate of the fundamental mode vibrationand the second overtone mode vibration of an amplification circuit, andβ₁ and β₂ are, respectively, a feedback rate of the fundamental modevibration and the second overtone mode vibration of a feedback circuit.

In other words, the quartz crystal oscillator is constructed so that aratio of the amplification rate α₁ of the fundamental mode vibration andthe amplification rate α₂ of the second overtone mode vibration of theamplification circuit is larger than that of the feedback rate β₂ of thesecond overtone mode vibration and the feedback rate β₁ of thefundamental mode vibration of the feedback circuit, and also a productof the amplification rate α₁ and the feedback rate β₁ of the fundamentalmode vibration is larger than 1. A description of the high frequencystability will be performed later.

Also, characteristics of the amplifier of the amplification circuitconstructing the quartz crystal oscillating circuit of this embodimentcan be expressed by negative resistance −RL_(i). For example, when i=1,negative resistance −RL₁ is for a fundamental mode vibration and wheni=2, negative resistance −RL₂ is for a second overtone mode vibration.In this embodiment, the quartz crystal oscillating circuit isconstructed so that a ratio of an absolute value of negative resistance,|−RL₁| of the fundamental mode vibration of the amplification circuitand series resistance R₁ of the fundamental mode vibration is largerthan that of an absolute value of negative resistance, |−RL₂| of thesecond overtone mode vibration of the amplification circuit and seriesresistance R₂ of the second overtone mode vibration. That is to say, theoscillating circuit is constructed so that it satisfies a relationshipof |−RL₁|/R₁>|−RL₂|/R₂. By constructing the oscillating circuit likethis, an oscillation of the second overtone mode can be suppressed, as aresult of which an output signal of a′ frequency of the fundamental modevibration can be provided because an oscillation of the fundamental modegenerates easily in the oscillating circuit.

FIG. 4 shows a general view of a flexural mode, quartz crystal tuningfork resonator 10 which is one of a contour mode resonator, constructinga quartz crystal oscillator, which constructs an electronic apparatus ofthe first embodiment of the present invention and its coordinate systemo-xyz. A cut angle θ which has a typical value of 0° to 10° is rotatedfrom a Z-plate perpendicular to the z axis about the x axis. Theresonator 10 comprises two tuning fork tines (vibrating tines) 20 and 26and a tuning fork base (a base) 40. The tines 20 and 26 have grooves 21and 27 respectively, with the grooves 21 and 27 extending into the base40. Also, the base 40 has the additional grooves 32 and 36. In addition,the tines 20 and 26 vibrate in a flexural mode of a fundamental mode andan inverse phase.

FIG. 5 shows a D-D′ cross-sectional view of the tuning fork base 40 ofthe quartz crystal resonator 10 in FIG. 4. In FIG. 5, the shape of theelectrode construction within the base 40 for the quartz crystalresonator of FIG. 4 is described in detail. The section of the base 40which couples to the tine 20 has the grooves 21 and 22 cut into theobverse and reverse faces of the base 40. Also, the section of the base40 which couples to the tine 26 has the grooves 27 and 28 cut into theobverse and reverse faces of the base 40. In addition to these grooves,the base 40 has the grooves 32 and 36 cut between the grooves 21 and 27,and also, the base 40 has the grooves 33 and 37 cut between the grooves22 and 28.

Furthermore, the grooves 21 and 22 have the first electrodes 23 and 24both of the same electrical polarity, the grooves 32 and 33 have thesecond electrodes 34 and 35 both of the same electrical polarity, thegrooves 36 and 37 have the third electrodes 38 and 39 both of the sameelectrical polarity, the grooves 27 and 28 have the fourth electrodes 29and 30 both of same electrical polarity and the sides of the base 40have the fifth and sixth electrodes 25 and 31, each of oppositeelectrical polarity. In more detail, the fifth, fourth, and secondelectrodes 25, 29, 30, 34 and 35 have the same electrical polarity,while the first, sixth and third electrodes 23, 24, 31, 38 and 39 havethe opposite electrical polarity to the others. Two electrode terminalsE-E′ are constructed. That is, the electrodes disposed inside thegrooves constructed opposite each other in the thickness (z axis)direction have the same electrical polarity. Also, the electrodesdisposed opposite each other across adjoining grooves have oppositeelectrical polarity.

In addition, the resonator has a thickness t of the tines or the tinesand the base, and a groove thickness t₁. It is needless to say that theelectrodes are disposed inside the grooves and on the sides of thetines. In this embodiment, the first electrodes 23 and 24 are disposedat the tine and the base, and also, the fourth electrodes 29 and 30 aredisposed at the tine and the base. In addition, the electrodes aredisposed on the sides of the tines opposite each other to the electrodesdisposed inside the grooves. Namely, the electrodes are disposedopposite each other inside the grooves and on the sides of the tines sothat the electrodes disposed opposite each other are of oppositeelectrical polarity. Additionally, electrodes are disposed facing eachother on the sides of the tines so that the electrodes disposed facingeach other are of opposite electrical polarity, and the tines arecapable of vibrating in inverse phase. In more detail, a first tuningfork tine and a second tuning fork tine, and a tuning fork base areformed integrally, an electrode is disposed on both sides of the firsttine and the second tine so that the electrodes disposed (facing eachother) on inner sides of the first and second tines are of oppositeelectrical polarity.

When a direct voltage is applied between the electrode terminals E-E′ (Eterminal: plus, E′ terminal: minus), an electric field E_(x) occurs inthe arrow direction as shown in FIG. 5. As the electric field E_(x)occurs perpendicular to the electrodes disposed on the base, theelectric field E_(x) has a very large value and a large distortionoccurs at the base, so that the quartz crystal tuning fork resonator isobtained with a small series resistance R₁ and a high quality factor Q₁,even if it is miniaturized.

FIG. 6 shows a plan view of the resonator 10 of FIG. 4. In FIG. 6, theconstruction and the dimension of grooves 21, 27, 32 and 36 aredescribed in detail. The groove 21 is constructed to include a portionof the central line 41 of the tine 20, and the groove 27 is similarlyconstructed to include a portion of the central line 42 of the tine 26.The width W₂ of the grooves 21 and 27 (groove width W₂) which include aportion of the central lines 41 and 42 respectively, is preferablebecause moment of inertia of the tines 20 and 26 becomes large and thetines can vibrate in a flexural mode easily. As a result, the quartzcrystal tuning fork resonator capable of vibrating in a fundamental modecan be obtained with a small series resistance R₁ and a high qualityfactor Q₁.

In more detail, when part widths W₁, W₃ and a groove width W₂ are taken,the tine width W of the tines 20 and 26 has a relationship ofW=W₁>W₂+W₃, and the part widths W₁, W₃ are constructed so that W₁≦W₃ orW₁<W₃. In addition, the groove width W₂ is constructed so that W₂≦W₁,W₃. In this embodiment, also, the grooves are constructed at the tinesso that a ratio (W₂/W) of the groove width W₂ and the tine width W islarger than 0.35 and less than 1, and a ratio (t₁/t) of the groovethickness t₁ and the thickness t of the tines (tine thickness t) is lessthan 0.79, to obtain very large moment of inertia of the tines. That is,the flexural mode, quartz crystal tuning fork resonator, capable ofvibrating in the fundamental mode, and having a good frequency stabilitycan be provided with a small series resistance R₁, a high quality factorQ₁ and a small capacitance ratio r₁ because electromechanicaltransformation efficiency of the resonator becomes large markedly.

Likewise, a length l_(i) of the grooves 21, 27 provided at the tines 20,26 extends into the base 40 in this embodiment (which has a dimension ofthe length l₂ and the length l₃ of the grooves). Therefore, a groovelength and a length of the tines are given by (l₁−l₃) and (l−l₂),respectively, and a ratio of (l₁−l₃) and (l−l₂) is within a range of 0.4to 0.8 to get a flexural mode tuning fork resonator with seriesresistance R₁ of a fundamental mode vibration smaller than seriesresistance R₂ of a second overtone mode vibration. Also, a length l₂ ofthe base is less than 0.5 mm.

Furthermore, the total length l is determined by the frequencyrequirement and the size of the housing case. Simultaneously, to get aflexural mode, quartz crystal tuning fork resonator, capable ofvibrating in a fundamental mode with suppression of the second overtonemode vibration which is an unwanted mode vibration, there is a closerelationship between the groove length l₁ and the total length l.Namely, a ratio (l₁/l) of the groove length l₁ and the total length l iswithin a range of 0.2 to 0.78 because the quantity of charges whichgenerate within the grooves and on the sides of the tines or the tinesand the base can be controlled by the ratio, as a result, the secondovertone mode vibration which is an unwanted mode vibration, can besuppressed, and simultaneously, a frequency stability of the fundamentalmode vibration gets high. Therefore, the flexural mode, quartz crystaltuning fork resonator, capable of vibrating easily in a fundamental modeand having high frequency stability can be provided. Also, the totallength l is less than 2.18 mm, preferably, within a range of 1.2 mm to 2mm, and groove length l₁ is less than 1.29 mm, preferably, within arange of 0.35 mm to 1.15 mm, to get a smaller-sized tuning forkresonator which vibrates in a flexural mode and a fundamental mode.

In more detail, series resistance R₁ of the fundamental mode vibrationbecomes smaller than series resistance R₂ of the second overtone modevibration. Namely, R₁<R₂, preferably, R₁<0.86R₂, therefore, a quartzcrystal oscillator comprising an amplifier (CMOS inverter), capacitors,resistors and a quartz crystal unit with the quartz crystal tuning forkresonator of this embodiment can be obtained, which is capable ofvibrating in the fundamental mode easily. In addition, in thisembodiment the grooves 21 and 27 of the tines 20 and 26 extend into thebase 40 in series, but embodiment of the present invention includes aplurality of grooves divided into the length direction of the tines. Inaddition, the grooves may be constructed only at the tines (l₃=0).

In this embodiment, the groove length l₁ corresponds to electrode lengthdisposed inside the grooves, though the electrode is not shown in FIG.6, but, when the electrode length is less than the groove length, thelength l₁ is of the electrode length. Namely, the ratio (l₁/l) in thiscase is expressed by a ratio of electrode length l₁ of the grooves andthe total length l. In order to achieve the above-mentioned object, itmay be satisfied with at least one groove with the ratio constructed atthe obverse and reverse faces of each tine. As a result, the flexuralmode, quartz crystal tuning fork resonator, capable of vibrating veryeasily in the fundamental mode and having the high frequency stabilitycan be realized. Also, a fork portion of this embodiment has arectangular shape, but this invention is not limited to this, forexample, the fork portion may have a U shape.

In addition, a space of between the tines is given by W₄, and in thisembodiment, the space W₄ and the groove width W₂ are constructed so thatW₄≧W₂, and more, the space W₄ is within a range of 0.05 mm to 0.35 mmand the groove width W₂ is within a range of 0.03 mm to 0.12 mm becauseit is easy to form a tuning fork shape and grooves of the tuning forktines separately by a photo-lithographic process and an etching process,consequently, a frequency stability for a fundamental mode vibrationgets higher than that for a second overtone mode vibration. In thisembodiment, a quartz wafer with the thickness t of 0.05 mm to 0.15 mm isused. In order to get a smaller-sized quartz crystal tuning forkresonator, capable of vibrating in a flexural mode, it is necessary thatgroove width W₂ is less than 0.7 mm and tine width W is less than 0.18mm, and preferably, the W is larger than 0.05 mm and less than 0.1 mm.Also, a groove thickness t₁ is within a range of 0.01 mm to 0.085 mmapproximately, and part widths W₁, W₃ are less than 0.021 mm,respectively, preferably, less than 0.015 mm. In addition, a grooveprovided on at least one of an obverse face and a reverse face of tuningfork tines of the present invention may be a through hole, namely, agroove thickness t₁=0.

In more detail, to obtain a flexural mode, quartz crystal tuning forkresonator with a high frequency stability which gives high timeaccuracy, it is necessary to obtain the resonator whose resonancefrequency is not influenced by shunt capacitance because quartz crystalis a piezoelectric material and the frequency stability is verydependent on the shunt capacitance. In order to decrease the influenceon the resonance frequency by the shunt capacitance, figure of meritM_(i) plays an important role. Namely, the figure of merit M_(i) thatexpresses inductive characteristics, electromechanical transformationefficiency and a quality factor of a flexural mode, quartz crystaltuning fork resonator, is defined by a ratio (Q_(i)/r_(i)) of a qualityfactor Q_(i) and capacitance ratio r_(i), namely, M_(i) is given byM_(i)=Q_(i)/r_(i), where i shows vibration order of the resonator, andfor example, when i=1 and 2, figures of merit M₁ and M₂ are a value fora fundamental mode vibration and a second overtone mode vibration of theflexural mode, quartz crystal tuning fork resonator, respectively.

Also, a frequency difference Δf of resonance frequency f_(s) ofmechanical series independent on the shunt capacitance and resonancefrequency f_(r) dependent on the shunt capacitance is inverselyproportional to the figure of merit M_(i). The larger the value M_(i)becomes, the smaller the difference Δf becomes. Namely, the influence onthe resonance frequency f_(r) by the shunt capacitance decreases becauseit is close to the resonance frequency f_(s). Accordingly, the largerthe M_(i) becomes, the higher the frequency stability of the flexuralmode, quartz crystal tuning fork resonator becomes because the resonancefrequency f_(r) of the resonator is almost never dependent on the shuntcapacitance. Namely, the quartz crystal tuning fork resonator can beprovided with a high time accuracy.

In detail, the flexural mode, quartz crystal tuning fork resonator canbe obtained with figure of merit M₁ of the fundamental mode vibrationlarger than figure of merit M₂ of the second overtone mode vibration bythe above-described tuning fork shape, grooves and dimensions. That isto say, a relationship of M₁>M₂ is obtained. As an example, whenresonance frequency of a flexural mode, quartz crystal tuning forkresonator is about 32.768 kHz for a fundamental mode vibration and theresonator has a value of W₂/W=0.5, t₁/t=0.34 and l₁/l=0.48, though thereis a distribution in production, the resonator has a value of M₁>65 andM₂<30, respectively.

Namely, the flexural mode, quartz crystal tuning fork resonator whichvibrates in the fundamental mode can be provided with high inductivecharacteristics, good electromechanical transformation efficiency (smallcapacitance ratio r₁ and small series resistance R₁) and a high qualityfactor. As a result, a frequency stability of the fundamental modevibration becomes higher than that of the second overtone modevibration, and simultaneously, the second overtone mode vibration can besuppressed because capacitance ratio r₂ and series resistance R₂ of thesecond overtone mode vibration become larger than capacitance ratio r₁and series resistance R₁ of the fundamental mode vibration,respectively. In particular, r₂ has a value larger than 1500 in thisembodiment.

Therefore, the resonator capable of vibrating in the fundamental modevibration can be provided with a high time accuracy because it has thehigh frequency stability. Consequently, a quartz crystal oscillatorcomprising the flexural mode, quartz crystal tuning fork resonator ofthis embodiment outputs an oscillation frequency of the fundamental modevibration as an output signal; and the frequency of the output signalhas a very high stability, namely, excellent time accuracy. In otherwords, the quartz crystal oscillator of this embodiment has a remarkableeffect such that a frequency change by ageing becomes extremely small.Also, an oscillation frequency of the resonator of this embodiment isadjusted so that a frequency deviation is within a range of −100 PPM to+100 PPM to a nominal frequency, e.g. 32.768 kHz, after mounting it at amounting portion of a case or a lid by conductive adhesives or solder.

In addition, the groove thickness t₁ of the present invention is thethinnest thickness of the grooves because quartz crystal is ananisotropic material and the groove thickness t₁ has a distribution whenit is formed by a chemical etching method. In detail, a groove shape ofthe sectional view of tuning fork tines in FIG. 5 has a rectangularshape, but the groove shape has an about U shape actually. In theabove-described embodiments, though the grooves are constructed at thetines, this invention is not limited to this, namely, a relationship ofthe figures of merit M₁ and M₂ can be applied to the conventionalflexural mode, quartz crystal tuning fork resonator and a relationshipof a quartz crystal oscillating circuit comprising an amplificationcircuit and a feedback circuit can be also applied to the conventionalflexural mode, quartz crystal tuning fork resonator to suppress a secondovertone Mode vibration and to get a high frequency stability for afundamental mode vibration of the tuning fork resonator.

FIG. 7 shows a plan view of a flexural mode, quartz crystal tuning forkresonator 45 which is one of a contour mode quartz crystal resonator,constructing a quartz crystal oscillator, which constructs an electronicapparatus of the second embodiment of the present invention. Theresonator 45 comprises tuning fork tines 46, 47 and a tuning fork base48. The tines 46, 47 and the base 48 are formed integrally by a chemicaletching process. In this embodiment, the base 48 has cut portions 53 and54. Also, a groove 49 is constructed to include a portion of the centralline 51 of the tine 46, and a groove 50 is similarly constructed toinclude a portion of the central line 52 of the tine 47. In thisembodiment, the grooves 49 and 50 are constructed at a part of the tines46 and 47, and have groove width W₂ and groove length l₁. In moredetail, a groove area S (=W₂×l₁) has a value of 0.025 mm² to 0.12 mm²because it is very easy to form the grooves by a chemical etchingprocess and the quartz crystal tuning fork resonator can be providedwith good electromechanical transformation efficiency by the formationof the grooves.

Namely, the quartz crystal tuning fork resonator, capable of vibratingin a fundamental mode and having a high frequency stability can beprovided with a small series resistance R₁ and a high quality factor Q₁.Therefore, a quartz crystal oscillator having the high frequencystability can be realized with an output signal of a frequency of thefundamental mode vibration. In this embodiment, though electrodes arenot shown in FIG. 7, the electrodes are disposed inside the grooves 49,50 and on sides of the tines 46 and 47, similar to the resonator of FIG.4. In detail, the electrodes are disposed opposite each other inside thegrooves and on the sides of the tines so that the electrodes disposedopposite each other are of opposite electrical polarity. In more detail,a groove is provided on both of an obverse face and a reverse face oftuning fork tines having a first tuning fork tine and a second tuningfork tine, and also, a first electrode is disposed inside the groove anda second electrode is disposed on both sides of the tuning fork tines.In addition, a quartz crystal tuning fork resonator has two electrodeterminals, the one of the electrode terminals comprises a firstelectrode disposed inside a groove provided on both of the obverse faceand the reverse face of the first tuning fork tine and a secondelectrode disposed on the both sides of the second tuning fork tine,such that the first and second electrodes are connected, and the otherof the electrode terminals comprises a second electrode disposed on theboth sides of the first tuning fork tine and a first electrode disposedinside a groove provided on both of the obverse face and the reverseface of the second tuning fork tine, such that the second and firstelectrodes are connected. In this embodiment, a groove is provided onboth of an obverse face and a reverse face of tuning fork tines, but thepresent invention in not limited to this, for example, a groove may beprovided on at least one of an obverse face and a reverse face of tuningfork tines.

In addition, the base 48 has cut portions 53 and 54, and the cut base 48has a dimension of width W₅ (tines side) and width W₆ (opposite side tothe tines side). When the base 48 is mounted at a mounting portion (e.g.on two lead wires for a package of a tubular type) of a case or a lid ofa surface mounting type or a tubular type by solder or conductiveadhesives, it is necessary to satisfy W₆≧W₅ to decrease energy losses byvibration. The cut portions 53 and 54 are very effective to decrease theenergy losses. Therefore, the flexural mode, quartz crystal tuning forkresonator, capable of vibrating in the fundamental mode and having thehigh frequency stability (high time accuracy) can be provided with asmall series resistance R₁ and a high quality factor Q₁. Also, the widthdimensions W=W₁+W₂+W₃ and W₄, and the length dimensions l₁, l₂ and l areas already described in relation to FIG. 6. In addition, a shape of thetuning fork base according to the present invention is not limited tothat of this embodiment, for example, a tuning fork base may have aframe portion protruding from the tuning fork base, and the frameportion is mounted at a mounting portion of a case or a lid of apackage.

FIG. 8 a and FIG. 8 b are a top view and a side view for alength-extensional mode quartz crystal resonator which is one of acontour mode resonator, constructing a quartz crystal oscillator, whichconstructs an electronic apparatus of the third embodiment of thepresent invention. The resonator 62 comprises a vibrational portion 63,connecting portions 66, 69 and supporting portions 67, 80 includingrespective mounting portions 68, 81. In addition, the supportingportions 67 and 80 have respective holes 67 a and 80 a. Also, electrodes64 and 65 are disposed opposite each other on upper and lower faces ofthe vibrational portion 63, and the electrodes have opposite electricalpolarities. Namely, a pair of electrodes is disposed on the vibrationalportion. In this case, a fundamental mode vibration can be excitedeasily.

In addition, the electrode 64 extends to the mounting portion 81 throughthe one connecting portion 69 and the electrode 65 extends to themounting portion 68 through the other connecting portion 66. In thisembodiment, the electrodes 64 and 65 disposed on the vibrational portion63 extend to the mounting portions of the different direction eachother. But, the electrodes may be constructed in the same direction. Theresonator in this embodiment is mounted on fixing portions of a case ora lid at the mounting portions 68 and 81 by conductive adhesives orsolder.

Here, a cutting angle of the length-extensional mode quartz crystalresonator is shown. First, a quartz crystal plate perpendicular to xaxis, so called, X plate quartz crystal is taken. Length L₀, width W₀and thickness T₀ which are each dimension of the X plate quartz crystalcorrespond to the respective directions of y, z and x axes.

Next, this X plate quartz crystal is, first, rotated with an angle θ_(x)of −30° to +30° about the x axis, and second, rotated with an angleθ_(y) of −40° to +40° about y′ axis which is the new axis of the y axis.In this case, the new axis of the x axis changes to x′ axis and the newaxis of the z axis changes to z″ axis because the z axis is rotatedtwice about two axes. The length-extensional mode quartz crystalresonator of the present invention is formed from the quartz crystalplate with the rotation angles.

In other words, according to an expression of IEEE notation, a cuttingangle of the resonator of the present invention can be expressed byXYtl(−30° to +30°)/(−40° to +40°). By choosing a cutting angle of theresonator, a turn over temperature point T_(p) can be taken at anarbitrary temperature. In this embodiment, length L₀, width W₀ andthickness T₀ correspond to y′, z″ and x′ axes, respectively. But, whenthe X plate is rotated once about the x axis, the z″ axis corresponds tothe z′ axis. In addition, the vibrational portion 63 has a dimension oflength L₀ greater than width W₀ and thickness T₀ smaller than the widthW₀. Namely, a coupling between length-extensional mode andwidth-extensional mode gets so small as it can be ignored, as a resultof which, the quartz crystal resonator can vibrate in a singlelength-extensional mode.

In more detail, resonance frequency of the length-extensional moderesonator is inversely proportional to length L₀, and it is almostindependent on such an other dimension as width W₀, thickness T₀,connecting portions and supporting potions. Also, in order to obtain alength-extensional mode quartz crystal resonator capable of vibrating ina fundamental mode with a frequency of 1 MHz to 10 MHz, the length L₀ iswithin a range of about 0.26 mm to about 2.7 mm. In addition, when alength-extensional mode resonator vibrates in an overtone mode, an oddnumber (n) pair of electrodes are disposed on a vibrational portion ofthe resonator, where n has a value of 1, 3, 5, . . . . In this case, thelength L₀ is a range of about (0.26 to 2.7) x n mm. Thus, the miniaturelength-extensional mode resonator can be provided with the frequency of1 MHz to 10 MHz.

Next, a value of a piezoelectric constant e₁₂ (=e′₁₂) is described,which is of great importance and necessary to excite a flexural mode,quartz crystal resonator and a length-extensional mode quartz crystalresonator of the present invention. The larger a value of thepiezoelectric constant e₁₂ becomes, the higher electromechanicaltransformation efficiency becomes. The piezoelectric constant e₁₂ of thepresent invention can be calculated using the piezoelectric constantse₁₁=0.171 C/m² and e₁₄=−0.0406 C/m² of quartz crystal. As a result, thepiezoelectric constant e₁₂ of the present invention is within a range of0.095 C/m² to 0.19 C/m² approximately in an absolute value. It is,therefore, easily understood that this value is enough large to obtain aflexural mode, quartz crystal tuning fork resonator and alength-extensional mode quartz crystal resonator with a small seriesresistance R₁ and a high quality factor Q. Especially, in order toobtain a flexural mode, quartz crystal tuning fork resonator with asmaller series resistance R₁, the e₁₂ is within a range of 0.12 C/m² to0.19 C/m² in the absolute value, and also, a groove and electrodes areprovided on at least one of an obverse face and a reverse face of tuningfork tines so that when each tuning fork tine is divided into twoportions (an inner portion located at a fork side and an outer portionlocated opposite to the fork side) versus a central line portionthereof, a value of e₁₂ of each portion of each tuning fork tine has anopposite sign each other. Namely, when the one of the two portions hase₁₂ of a plus sign, the other of the two portions has e₁₂ of a minussign. In more detail, a groove and electrodes are provided at tuningfork tines so that a sign of e₁₂ of inner portions of each tuning forktine is opposite to the sign of e₁₂ of outer portions of each tuningfork tine.

When an alternating current voltage is applied between the electrodes 64and 65 shown in FIG. 8 b, an electric field E_(x) occurs alternately inthe thickness direction, as shown by the arrow direction of the solidand broken lines in FIG. 8 b. Consequently, the vibrational portion 63is capable of extending and contracting in the length direction.

FIG. 9 shows a cross-sectional view of a quartz crystal unitconstructing a quartz crystal oscillator, which constructs an electronicapparatus of the fourth embodiment of the present invention. The quartzcrystal unit 170 comprises a contour mode quartz crystal resonator 70 ora thickness shear mode quartz crystal resonator 70, a case 71 and a lid72. In more detail, the resonator 70 is mounted at a mounting portion 74of the case 71 by conductive adhesives 76 or solder. Also, the case 71and the lid 72 are connected through a connecting member 73. Forexample, the contour mode resonator 70 in this embodiment is the sameresonator as one of the flexural mode, quartz crystal tuning forkresonators 10 and 45 described in detail in FIG. 4-FIG. 7. Also, in thisembodiment, circuit elements are connected at outside of the quartzcrystal unit to get a quartz crystal oscillator. Namely, only the quartzcrystal tuning fork resonator is housed in the unit and also, it ishoused in the unit in vacuum. In this embodiment, the quartz crystalunit of a surface mounting type is shown, but the quartz crystal tuningfork resonator may be housed in a tubular type, namely a quartz crystalunit of the tubular type. Also, instead of the flexural mode, quartzcrystal tuning fork resonator and the thickness shear mode quartzcrystal resonator, one of a length-extensional mode quartz crystalresonator, a width-extensional mode quartz crystal resonator and a Lamemode quartz crystal resonator which are a contour mode resonator,respectively, or a SAW (Surface Acoustic Wave) resonator may be housedin the unit. In addition, the present invention is not limited to thequartz crystal unit having the contour mode quartz crystal resonator orthe thickness shear mode quartz crystal resonator in this embodiment,for example, the present invention also includes a quartz crystal unithaving a piezoelectric filter, e.g. a SAW piezoelectric filter or apiezoelectric sensor, e.g. an angular velocity piezoelectric sensor.

In addition, a member of the case and the lid is ceramics or glass and ametal or glass, respectively, and a connecting member is a metal orglass with low melting point. Also, a relationship of the resonator, thecase and the lid described in this embodiment is applied to a quartzcrystal oscillator of the present invention which will be described inFIG. 10.

FIG. 10 shows a cross-sectional view of a quartz crystal oscillator,which constructs an electronic apparatus of the fifth embodiment of thepresent invention. The quartz crystal oscillator 190 comprises a quartzcrystal oscillating circuit, a case 91 and a lid 92. In this embodiment,circuit elements constructing the oscillating circuit are housed in aquartz crystal unit comprising a contour mode quartz crystal resonator90 or a thickness shear mode quartz crystal resonator 90, the case 91and the lid 92. Also, the oscillating circuit of this embodimentcomprises an amplifier 98 including a feedback resistor, the resonator90, capacitors (not shown here) and a drain resistor (not shown here),and a CMOS inverter is used as the amplifier 98.

In addition, in this embodiment, the resonator 90 is mounted at amounting portion 94 of the case 91 by conductive adhesives 96 or solder.As described above, the amplifier 98 is housed in the quartz crystalunit and mounted at the case 91. Also, the case 91 and the lid 92 areconnected through a connecting member 93. For example, the contour moderesonator 90 of this embodiment is the same as one of the flexural mode,quartz crystal tuning fork resonators 10 and 45 described in detail inFIG. 4-FIG. 7. Also, instead of the flexural mode, quartz crystal tuningfork resonator and the thickness shear mode quartz crystal resonator,one of a length-extensional mode quartz crystal resonator, awidth-extensional mode quartz crystal resonator and a Lame mode quartzcrystal resonator which are a contour mode resonator, respectively, or aSAW (Surface Acoustic Wave) resonator may be housed in the unit.

Likewise, in this embodiment, a piece of flexural mode, quartz crystaltuning fork resonator is housed in the unit, but the present inventionalso includes a quartz crystal unit having a plurality of flexural mode,quartz crystal tuning fork resonators, and at least two of the pluralityof resonators are connected electrically in parallel. In addition, theat least two resonators may be an individual resonator or may beindividual resonators that are formed integrally at each tuning basethrough a connecting portion.

Next, a method for manufacturing a quartz crystal oscillator, whichconstructs an electronic apparatus of the present invention, isdescribed in detail, according to the manufacturing steps.

FIG. 11 shows an embodiment of a method for manufacturing a quartzcrystal oscillator, which constructs an electronic apparatus of thepresent invention and a step diagram embodying the present invention.The signs of S-1 to S-12 are the step numbers. First, S-1 shows across-sectional view of a quartz crystal wafer 140. Next, in S-2 metalfilm 141, for example, chromium and gold on the chromium are,respectively, disposed on upper and lower faces of the quartz crystalwafer 140 by an evaporation method or a spattering method. In addition,resist 142 is spread on said metal film 141 in S-3, and after the metalfilm 141 and the resist 142 were removed except those of tuning forkshape by a photo-lithographic process and an etching process, the tuningfork shape with tuning fork tines 143, 144 and a tuning fork base 145,as be shown in S-4, is integrally formed by a chemical etching process.When the tuning fork shape is formed, cut portions may be formed at thetuning fork base. In FIG. 11, the formation of a piece of tuning forkshape is shown, but, a number of tuning fork shapes are actually formedin a piece of quartz crystal wafer.

Similar to the steps of S-2 and S-3, metal film and resist are spreadagain on the tuning fork shape of S-4 and grooves 146, 147, 148 and 149each of which has two step difference portions along the lengthdirection of the tuning fork tines, are formed at the tuning fork tines143, 144 by the photo-lithographic process and the etching process, andthe shape of S-5 is obtained after all of the resist and the metal filmwere removed. In addition, metal film and resist are spread again on theshape of S-5 and electrodes which are of opposite electrical polarity,are disposed on sides of the tines and inside the grooves thereof, as beshown in S-6.

Namely, electrodes 150, 153 disposed on the sides of the tuning forktine 143 and electrodes 155, 156 disposed inside the grooves 148, 149 ofthe tuning fork tine 144 have the same electrical polarity. Similarly,electrodes 151, 152 disposed inside the grooves 146, 147 of the tuningfork tine 143 and electrodes 154, 157 disposed on the sides of thetuning fork tine 144 have the same electrical polarity. Two electrodeterminals are, therefore, constructed. In more detail, when analternating current (AC) voltage is applied between the terminals, thetuning fork tines vibrate in a flexural mode of an inverse phase becausesaid electrodes disposed on step difference portions of the grooves andthe electrodes disposed opposite to the said electrodes have oppositeelectrical polarity. In the step of S-6, a piece of quartz crystaltuning fork resonator, capable of vibrating in a flexural mode is shownin the quartz crystal wafer, but a number of quartz crystal tuning forkresonators are actually formed in the wafer.

In addition, a resonance (oscillation) frequency for said resonators isadjusted by a separate step of at least twice and the first adjustmentof resonance frequency for said resonators is performed in the quartzcrystal wafer by a laser method or an evaporation method or an ionetching method so that a frequency deviation of said resonators iswithin a range of −9000 PPM to +5000 PPM (Parts Per Million) to anominal frequency of 10 kHz to 200 kHz, e.g. 32.768 kHz. The adjustmentof frequency by the laser or ion etching method is performed by trimmingmass disposed on tuning fork tines and the adjustment of frequency bythe evaporation method is performed by adding mass on tuning fork tines.Namely, those methods can change the resonance (oscillation) frequencyof said resonators. Also, the resonators formed in the quartz crystalwafer are inspected therein and when there is a failure resonator, it isremoved from the wafer or something is marked on it or it is rememberedby a computer.

In this embodiment, the tuning fork shape is formed from the step of S-3and after that, the grooves are formed at the tuning fork tines, namely,the tuning fork tines are formed before the grooves are formed, but thisinvention is not limited to said embodiment, for example, the groovesare first formed from the step of S-3 and after that, the tuning forkshape may be formed, namely, the grooves are formed before the tuningfork tines are formed. Also, the tuning fork shape and the grooves maybe formed simultaneously, namely, the tuning fork tines and the groovesare formed simultaneously.

There are two methods of A and B in the following step, as be shown byarrow signs. For the step of A, the tuning fork base 145 of the formedflexural mode, quartz crystal tuning fork resonator 160 is first mountedon mounting portion 159 of a case 158 by conductive adhesives 161 orsolder, as be shown in S-7. Next, the second adjustment of resonance(oscillation) frequency for the resonator 160 is performed by laser 162or evaporation or ion etching method in S-8 so that a frequencydeviation is within a range of −100 PPM to +100 PPM to the nominalfrequency of 10 kHz to 200 kHz, e.g. 32.768 kHz. Finally, the case 158and a lid 163 are connected via glass 164 with the low melting point ora metal in S-9. In this case, the connection of the case and the lid isperformed in vacuum because the case 158 has no hole to close it invacuum.

In addition, though it is not visible in FIG. 11, the third frequencyadjustment may be performed by laser after the step of the connection ofS-9 to get a small frequency deviation to the nominal frequency when amaterial of the lid is glass. As a result of which it is possible to getthe resonator with the frequency deviation which is within a range of−50 PPM to +50 PPM to the nominal frequency of 10 kHz to 200 kHz, e.g.32.768 kHz. Namely, the nominal frequency, capable of vibrating in afundamental mode is less than 200 kHz. In this step, when the thirdfrequency adjustment is performed, a/an resonance (oscillation)frequency of said resonators is adjusted so that the frequency deviationby the second frequency adjustment is within a range of −950 PPM to +950PPM to the nominal frequency, e.g. 32.768 kHz.

For the step of B, the tuning fork base 145 of the formed resonator 160is first mounted on a mounting portion 159 of a case 165 by conductiveadhesives 161 or solder in S-10, in addition, in S-11 the case 165 and alid 163 are connected by the same way as that of S-9, in more detail,after the resonator was mounted on the mounting portion of the case orafter the resonator was mounted at the mounting portion, and the caseand the lid were connected, the second adjustment of resonance(oscillation) frequency is performed so that a frequency deviation isgenerally within a range of −100 PPM to +100 PPM to a nominal frequencyof 10 kHz to 200 kHz, e.g. 32.768 kHz in vacuum, but, it may be within awider range, for example, −950 PPM to +950 PPM when the third frequencyadjustment as will be shown as follows, is performed. Finally, a hole167 constructed at the case 165 is closed in vacuum using such a metal166 as solder or glass with the low melting point in S-12.

Also, similar to the step of A, the third adjustment of resonance(oscillation) frequency may be performed by laser after the step of S-12to get a small frequency deviation to the nominal frequency. As a resultof which it is possible to get the resonator with the frequencydeviation which is within a range of −50. PPM to +50 PPM to the nominalfrequency, e.g. 32.768 kHz. Thus, a frequency deviation of theresonators in the case of A and B is finally within a range of −100 PPMto +100 PPM at most. Also, the second frequency adjustment may beperformed after the case and the lid were connected and the hole wasclosed in vacuum. In addition, the hole is constructed at the case, butmay be constructed at the lid. Also, the frequency adjustment of thepresent invention is performed in vacuum or inert gas such as nitrogengas or atmosphere, and the values described above are values in vacuum.

Therefore, the flexural mode, quartz crystal tuning fork resonators andthe quartz crystal units manufactured by the above-described method areminiaturized and realized with a small series resistance R₁, a highquality factor Q₁ and low price.

Moreover, in the above-described embodiment, though the first frequencyadjustment of the resonators is performed in the quartz crystal waferand at the same time, when there is a failure resonator, something ismarked on it or it is removed from the quartz crystal wafer, but thepresent invention is not limited to this, namely, the present inventionmay include the step to inspect the flexural mode, quartz crystal tuningfork resonators formed in the quartz crystal wafer therein, in otherwords, the step to inspect whether there is a failure resonator or notin the quartz crystal wafer. When there is a failure resonator in thewafer, something is marked on it or it is removed from the wafer or itis remembered by a computer. By including the step, it can increase theyield because it is possible to find out the failure resonator in anearly step and the failure resonator does not go to the next step. As aresult of which low priced flexural mode, quartz crystal tuning forkresonators can be provided with excellent electrical characteristics.

In this embodiment, the frequency adjustment is performed three times bya separate step, but may be performed at least twice by a separate step.For example, the third frequency adjustment may be omitted. In addition,in order to construct a quartz crystal oscillator, two electrodeterminals of the resonators are connected electrically to an amplifier,capacitors and resistors. In other words, a quartz crystal oscillatingcircuit is constructed and connected electrically so that anamplification circuit comprises a CMOS inverter and a feedback resistorand a feedback circuit comprises a flexural mode, quartz crystal tuningfork resonator, a drain resistor, a capacitor of a gate side and acapacitor of a drain side. Also, the third frequency adjustment may beperformed after the quartz crystal oscillating circuit was constructedin a quartz crystal unit.

Likewise, the flexural mode quartz crystal resonator of a tuning forktype has two tuning fork tines in the present embodiments, butembodiments of the present invention include tuning fork tines more thantwo. In addition, the quartz crystal tuning fork resonators of thepresent embodiments are housed in a package (unit) of a surface mountingtype comprising a case and a lid, but may be housed in a package of atubular type.

In addition, for the tuning fork resonators constructing the quartzcrystal oscillators of the first embodiment to the fourth embodiment ofthe present invention, the resonators are provided so that a capacitanceratio r₁ of a fundamental mode vibration gets smaller than a capacitanceratio r₂ of a second overtone mode vibration, in order to obtain afrequency change of the fundamental mode vibration larger than that ofthe second overtone mode vibration, versus the same change of a value ofload capacitance C_(L). Namely, a variable range of a frequency of thefundamental mode vibration gets wider than that of the second overtonemode vibration.

In more detail, for example, when C_(L)=18 pF and the C_(L) changes in 1pF, the frequency change of the fundamental mode vibration becomeslarger than that of the second overtone mode vibration because thecapacitance ratio r₁ is smaller than the capacitance ratio r₂.Therefore, there is a remarkable effect for the fundamental modevibration, such that the resonators can be provided with the frequencyvariable in the wide range, even when the value of load capacitanceC_(L) changes slightly. Accordingly, when a variation of the samefrequency is required, the number of capacitors which are used in thequartz crystal oscillators decreases because the frequency change versusload capacitance 1 pF becomes large, as compared with that of the secondovertone mode vibration. As a result, the low priced oscillators can beprovided.

Moreover, capacitance ratios r₁ and r₂ of a flexural mode, quartzcrystal tuning fork resonator are given by r₁=C₀/C₁ and r₂=C₀/C₂,respectively, where C₀ is shunt capacitance in an electrical equivalentcircuit of the resonator, and C₁ and C₂ are, respectively, motionalcapacitance of a fundamental mode vibration and a second overtone modevibration in the electrical equivalent circuit of the resonator. Inaddition, the flexural mode, quartz crystal tuning fork resonator has aquality factor Q₁ for the fundamental mode vibration and a qualityfactor Q₂ for the second overtone mode vibration.

In detail, the tuning fork resonator of this embodiment is provided sothat the influence on resonance frequency of the fundamental modevibration by the shunt capacitance becomes smaller than that of thesecond overtone mode vibration by the shunt capacitance, namely, so thatit satisfies a relationship of S₁=r₁/2Q₁ ²<S₂=r₂/2Q₂ ², preferably,S₁<S₂/2. As a result, the tuning fork resonator, capable of vibrating inthe fundamental mode and having a high frequency stability can beprovided because the influence on the resonance frequency of thefundamental mode vibration by the shunt capacitance becomes so extremelysmall as it can be ignored. Also, the present invention replaces r₁/2Q₁² with S₁ and r₂/2Q₂ ² with S₂, respectively, and here, S₁ and S₂ arecalled “a stable factor of frequency” of the fundamental mode vibrationand the second overtone mode vibration.

In addition, when a power source is applied to the quartz crystaloscillating circuit, at least one oscillation which satisfies anamplitude condition and a phase condition of vibration starts in thecircuit, and a spent time to get to about ninety percent of the steadyamplitude of the vibration is called “rise time”. Namely, the shorterthe rise time becomes, the easier the oscillation becomes. When risetime t_(r1) of the fundamental mode vibration and rise time t_(r2) ofthe second overtone mode vibration in the circuit are taken, t_(r1) andt_(r2) are given by t_(r1)=kQ₁/(ω₁(−1+|−RL₁|/R₁)) andt_(r2)=kQ₂/(ω₂(−1+|−RL₂|/R₂)), respectively, where k is constant and ω₁and ω₂ are an angular frequency for the fundamental mode vibration andthe second overtone mode vibration, respectively.

From the above-described relation, it is possible to obtain the risetime t_(r1) of the fundamental mode vibration less than the rise timet_(r2) of the second overtone mode vibration. As an example, whenresonance (oscillation) frequency of a flexural mode, quartz crystaltuning fork resonator is about 32.768 kHz for a fundamental modevibration and the resonator has a value of W₂/W=0.5, t₁/t=0.34 andl₁/l=0.48, though there is a distribution in production, as an example,the resonator has a value of Q₁=62,000 and Q₂=192,000, respectively. Inthis embodiment, Q₂ has a value of about three times of Q₁. Accordingly,to obtain the t_(r1) less than the t_(r2), it is necessary to satisfy arelationship of |−RL₁|/R₁>2|−RL₂|/R₂−1 by using a relation of ω₂=6ω₁approximately. Also, according to this invention, the relationship isnot limited to the quartz crystal oscillating circuit comprising theresonator in this embodiment, but this invention also includes allquartz crystal oscillating circuits to satisfy the relationship. Byconstructing the oscillating circuit like this, a quartz crystaloscillator with the flexural mode, quartz crystal tuning fork resonatorcan be provided with a short rise time. In other words, an output signalof the oscillator has an oscillation frequency of the fundamental modevibration of the resonator and is outputted through a buffer circuit.Namely, the second overtone mode vibration can be suppressed in theoscillating circuit. In this embodiment, the resonator has also a valueof r₁=320 and r₂=10,600 as an example. According to this invention, r₁has a value of 210 to 520.

The above-described quartz crystal resonators are formed by at least onemethod of chemical, mechanical and physical methods. The mechanicalmethod, for example, uses a particle such as GC#1000 and the physicalmethod, for example, uses atom or molecule. Therefore, these methods arecalled “a particle method” here.

Thus, the electronic apparatus of this invention comprising a displayportion and a quartz crystal oscillator at least may operate normallybecause the quartz crystal oscillator comprises the quartz crystaloscillating circuit with a high frequency stability, namely, a highfrequency reliability.

As described above, it will be easily understood that the electronicapparatus comprising the quartz crystal oscillator comprising the quartzcrystal oscillating circuit having the flexural mode, quartz crystaltuning fork resonator with novel shapes, the novel electrodeconstruction and excellent electrical characteristics, according to thepresent invention, may have the outstanding effects. Similar to this, itwill be easily understood that the electronic apparatus comprising thequartz crystal oscillator comprising the quartz crystal oscillatingcircuit having the length-extensional mode quartz crystal resonator withthe novel cutting angle and the novel shape, according to the presentinvention, may have also the outstanding effect. In addition to this,while the present invention has been shown and described with referenceto preferred embodiments thereof, it will be understood by those skilledin the art that the changes in shape and electrode construction can bemade therein without departing from the spirit and scope of the presentinvention.

1. A method for manufacturing a quartz crystal unit, comprising thesteps of : forming a quartz crystal tuning fork resonator capable ofvibrating in a flexural mode of an inverse phase and having a quartzcrystal tuning fork shape, a capacitance ratio r₁ of a fundamental modeof vibration and a capacitance ratio r₂ of a second overtone mode ofvibration, the quartz crystal tuning fork shape having a dimension and aquartz crystal tuning fork base, and first and second quartz crystaltuning fork tines connected to the quartz crystal tuning fork base, eachof the first and second quartz crystal tuning fork tines having oppositemain surfaces and opposite side surfaces; forming at least one groovehaving a dimension in at least one of the opposite main surfaces of eachof the first and second quartz crystal tuning fork tines so that aspaced-apart distance between the first and second quartz crystal tuningfork tines is greater than or equal to a width of the at least onegroove formed in the at least one of the opposite main surfaces of eachof the first and second quartz crystal tuning fork tines; determiningthe dimension of each of the quartz crystal tuning fork shape and the atleast one groove formed in the at least one of the opposite mainsurfaces of each of the first and second quartz crystal tuning forktines so that the capacitance ratio r₁ of the fundamental mode ofvibration of the quartz crystal tuning fork resonator is less than thecapacitance ratio r₂ of the second overtone mode of vibration thereof;providing a case having a mounting portion and a lid for covering anopen end of the case; mounting the quartz crystal tuning fork resonatoron the mounting portion of the case; and connecting the lid to the caseto cover the open end of the case.
 2. A method according to claim 1;wherein the opposite main surfaces comprise a first main surface and asecond main surface; wherein the forming step of the at least one grooveincludes the step of forming a plurality of grooves divided in thelength direction in at least one of the first and second main surfacesof each of the first and second quartz crystal tuning fork tines so thata width of at least one of the grooves formed in the at least one of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines is within a range of 0.03 mm to 0.12 mm.
 3. Amethod according to claim 1; wherein the opposite main surfaces comprisea first main surface and a second main surface; and further comprisingthe steps of forming a groove having a dimension in each of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines; forming an electrode having a dimension on a surfaceof the groove formed in each of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines so thatthe electrode formed on the surface of the groove formed in each of thefirst and second main surfaces of the first quartz crystal tuning forktine has an electrical polarity opposite to an electrical polarity ofthe electrode formed on the surface of the groove formed in each of thefirst and second main surfaces of the second quartz crystal tuning forktine; and determining the dimension of each of the quartz crystal tuningfork shape, the groove formed in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines and the electrode formed on the surface of the groove formed ineach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that the capacitance ratio r₁of the fundamental mode of vibration of the quartz crystal tuning forkresonator is less than the capacitance ratio r₂ of the second overtonemode of vibration thereof.
 4. A method according to claim 1; wherein theopposite main surfaces comprise a first main surface and a second mainsurface and the opposite side surfaces have a first side surface and asecond side surface; and further comprising the sequential steps offorming the quartz crystal tuning fork shape having the quartz crystaltuning fork base, and the first and second quartz crystal tuning forktines in a first etching process; forming a groove in at least one ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines in a second etching process differentfrom the first etching process so that the spaced-apart distance betweenthe first and second quartz crystal tuning fork tines is greater than awidth of the groove formed in the at least one of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines; disposing at least one metal film on each of the first and secondmain surfaces and the first and second side surfaces of each of thefirst and second quartz crystal tuning fork tines and a surface of thegroove formed in the at least one of the first and second main surfacesof each of the first and second quartz crystal tuning fork tines;disposing a resist on the at least one metal film; forming a firstelectrode on the surface of the groove formed in the at least one of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines and a second electrode on each of the firstand second side surfaces of each of the first and second quartz crystaltuning fork tines so that the first electrode has an electrical polarityopposite to an electrical polarity of the second electrode; removing theresist disposed on the at least one metal film; mounting the quartzcrystal tuning fork resonator on the mounting portion of the case;adjusting an oscillation frequency of the quartz crystal tuning forkresonator; and connecting the lid to the case to cover the open end ofthe case after the adjusting step of the oscillation frequency.
 5. Amethod according to claim 4; wherein the groove is formed in each of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines so that a width of the groove formed in eachof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines is within a range of 0.03 mm to 0.12 mmand a length of the groove formed in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines is within a range of 0.35 mm to 1.15 mm.
 6. A method according toclaim 4; wherein a plurality of grooves having a first groove and asecond groove divided in the length direction is formed in at least oneof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines so that a width of at least one of thefirst and second grooves formed in the at least one of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines is within a range of 0.03 mm to 0.12 mm.
 7. A methodaccording to claim 4; wherein the quartz crystal tuning fork base has alength l₂ less than 0.5 mm; and wherein the groove is formed in each ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines so that a distance in the widthdirection of the groove measured from an outer edge of the groove to anouter edge of the corresponding one of the first and second quartzcrystal tuning fork tines is less than 0.015 mm.
 8. A method accordingto claim 4; wherein the case has a through-hole; and further comprisingthe sequential steps of removing the resist disposed on the at least onemetal film; mounting the quartz crystal tuning fork resonator on themounting portion of the case; adjusting the oscillation frequency of thequartz crystal tuning fork resonator so that the oscillation frequencyis about 32.768 kHz with a frequency deviation within a range of −100ppm to +100 ppm; connecting the lid to the case to cover the open end ofthe case; and disposing a metal or a glass into the through-hole of thecase to close the through-hole in a vacuum.
 9. A method according toclaim 4; wherein the case has no through-hole; and further comprisingthe sequential steps of removing the resist disposed on the at least onemetal film; mounting the quartz crystal tuning fork resonator on themounting portion of the case; adjusting the oscillation frequency of thequartz crystal tuning fork resonator so that the oscillation frequencyis about 32.768 kHz with a frequency deviation within a range of −100ppm to +100 ppm; and connecting the lid to the case to cover the openend of the case.
 10. A method according to claim 4; wherein each of thefirst and second main surfaces has a central linear portion; wherein thegroove is formed in the central linear portion of at least one of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines so that the spaced-apart distance between thefirst and second quartz crystal tuning fork tines is within a rage of0.05 mm to 0.35 mm, a distance in the width direction of the groovemeasured from a first outer edge of the groove to a first outer edge ofthe corresponding one of the first and second quartz crystal tuning forktines being defined by W₁ and a distance in the width direction of thegroove measured from a second outer edge opposite the first outer edgeof the groove to a second outer edge opposite the first outer edge ofthe corresponding one of the first and second quartz crystal tuning forktines being defined by W₃; and wherein the groove is formed in thecentral linear portion of each of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines so that awidth of the groove formed in the central linear portion of each of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines is less than 0.07 mm and W₁ is equal to W₃.11. A method according to claim 1; wherein the case has a through-hole;wherein the opposite main surfaces comprise a first main surface and asecond main surface and the opposite side surfaces have a first sidesurface and a second side surface; and further comprising the sequentialsteps of forming the quartz crystal tuning fork shape having the quartzcrystal tuning fork base, and the first and second quartz crystal tuningfork tines in a first etching process; forming a groove in at least oneof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines in a second etching process differentfrom the first etching process so that the spaced-apart distance betweenthe first and second quartz crystal tuning fork tines is greater than awidth of the groove formed in the at least one of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines; disposing at least one metal film on each of the first and secondmain surfaces and the first and second side surfaces of each of thefirst and second quartz crystal tuning fork tines and a surface of thegroove formed in the at least one of the first and second main surfacesof each of the first and second quartz crystal tuning fork tines;disposing a resist on the at least one metal film; forming a firstelectrode on the surface of the groove formed in the at least one of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines and a second electrode on each of the firstand second side surfaces of each of the first and second quartz crystaltuning fork tines so that the first electrode has an electrical polarityopposite to an electrical polarity of the second electrode; mounting thequartz crystal tuning fork resonator on the mounting portion of thecase; connecting the lid to the case to cover the open end of the case;and disposing a metal or a glass into the through-hole of the case toclose the through-hole in a vacuum.
 12. A method according to claim 11further comprising the step of adjusting in a vacuum an oscillationfrequency of the quartz crystal tuning fork resonator after theconnecting step of the lid and the case and before the disposing step ofthe metal or the glass.
 13. A method according to claim 11; wherein thegroove is formed in each of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines so that a widthof the groove formed in each of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines is withina range of 0.03 mm to 0.12 mm and a length of the groove formed in eachof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines is within a range of 0.35 mm to 1.15mm.
 14. A method according to claim 11; further comprising the step ofadjusting an oscillation frequency of the quartz crystal tuning forkresonator after the disposing step of the metal or the glass so that theoscillation frequency is about 32.768 kHz with a frequency deviationwithin a range of −50 ppm to +50 ppm.
 15. A method according to claim 1;wherein the opposite main surfaces comprise a first main surface and asecond main surface and the opposite side surfaces have a first sidesurface and a second side surface; and further comprising the sequentialsteps of forming simultaneously the quartz crystal tuning fork shapehaving the quartz crystal tuning fork base, and the first and secondquartz crystal tuning fork tines and a groove in at least one of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines in an etching process so that the spaced-apartdistance between the first and second quartz crystal tuning fork tinesis greater than a width of the groove formed in the at least one of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines; disposing at least one metal film on each ofthe first and second main surfaces and the first and second sidesurfaces of each of the first and second quartz crystal tuning forktines and a surface of the groove formed in the at least one of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines; disposing a resist on the at least one metalfilm; forming a first electrode on the surface of the groove formed inthe at least one of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines and a second electrodeon each of the first and second side surfaces of each of the first andsecond quartz crystal tuning fork tines so that the first electrode hasan electrical polarity opposite to an electrical polarity of the secondelectrode; mounting the quartz crystal tuning fork resonator on themounting portion of the case; and connecting the lid to the case tocover the open end of the case.
 16. A method according to claim 1;wherein the quartz crystal tuning fork resonator has a merit value M₁ ofthe fundamental mode of vibration and a merit value M₂ of the secondovertone mode of vibration, the merit value M₁ being defined by theratio (Q₁/r₁) and the merit value M₂ being defined by the ratio (Q₂/r₂),where Q₁ and Q₂ represent a quality factor of the fundamental mode ofvibration and the second overtone mode of vibration, respectively, ofthe quartz crystal tuning fork resonator and r₁ and r₂ represent thecapacitance ratio of the fundamental mode of vibration and the secondovertone mode of vibration, respectively, of the quartz crystal tuningfork resonator; wherein the opposite main surfaces comprise a first mainsurface and a second main surface; and further comprising the steps offorming a groove having a dimension in at least one of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines; forming an electrode on a surface of the grooveformed in the at least one of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines so that theelectrode formed on the surface of the groove formed in the at least oneof the first and second main surfaces of the first quartz crystal tuningfork tine has an electrical polarity opposite to an electrical polarityof the electrode formed on the surface of the groove formed in the atleast one of the first and second main surfaces of the second quartzcrystal tuning fork tine; and determining the dimension of each of thequartz crystal tuning fork shape and the groove formed in the at leastone of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that the merit value M₁ ofthe fundamental mode of vibration of the quartz crystal tuning forkresonator is greater than the merit value M₂ of the second overtone modeof vibration thereof.
 17. A method according to claim 1; wherein theopposite main surfaces comprise a first main surface and a second mainsurface; wherein the quartz crystal tuning fork resonator has a seriesresistance R₁ of the fundamental mode of vibration and a seriesresistance R₂ of the second overtone mode of vibration; and furthercomprising the steps of forming the quartz crystal tuning fork resonatorhaving an overall length; forming a groove having a length in each ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines; and determining the length of thegroove formed in each of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines and the overalllength of the quartz crystal tuning fork resonator so that the seriesresistance R₁ of the fundamental mode of vibration of the quartz crystaltuning fork resonator is less than the series resistance R₂ of thesecond overtone mode of vibration thereof.
 18. A method formanufacturing a quartz crystal resonator, comprising the steps offorming a quartz crystal tuning fork resonator capable of vibrating in aflexural mode of an inverse phase and having a quartz crystal tuningfork shape, a capacitance ratio r₁ of a fundamental mode of vibrationand a capacitance ratio r₂ of a second overtone mode of vibration, thequartz crystal tuning fork shape having a dimension and a quartz crystaltuning fork base, and first and second quartz crystal tuning fork tinesconnected to the quartz crystal tuning fork base, each of the first andsecond quartz crystal tuning fork tines having opposite main surfacesand opposite side surfaces; forming at least one groove having adimension in at least one of the opposite main surfaces of each of thefirst and second quartz crystal tuning fork tines so that a spaced-apartdistance between the first and second quartz crystal tuning fork tinesis greater than or equal to a width of the at least one groove formed inthe at least one of the opposite main surfaces of each of the first andsecond quartz crystal tuning fork tines; and determining the dimensionof each of the quartz crystal tuning fork shape and the at least onegroove formed in the at least one of the opposite main surfaces of eachof the first and second quartz crystal tuning fork tines so that thecapacitance ratio r₁ of the fundamental mode of vibration of the quartzcrystal tuning fork resonator is less than the capacitance ratio r₂ ofthe second overtone mode of vibration thereof.
 19. A method according toclaim 18; wherein the opposite main surfaces comprise a first mainsurface and a second main surface; and further comprising the steps offorming a groove having a dimension in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines; forming an electrode having a dimension on a surface of thegroove formed in each of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines so that theelectrode formed on the surface of the groove formed in each of thefirst and second main surfaces of the first quartz crystal tuning forktine has an electrical polarity opposite to an electrical polarity ofthe electrode formed on the surface of the groove formed in each of thefirst and second main surfaces of the second quartz crystal tuning forktine; and determining the dimension of each of the quartz crystal tuningfork shape, the groove formed in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines and the electrode formed on the surface of the groove formed ineach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that the capacitance ratio r₁of the fundamental mode of vibration of the quartz crystal tuning forkresonator is less than the capacitance ratio r₂ of the second overtonemode of vibration thereof.
 20. A method according to claim 18; whereinthe opposite main surfaces comprise a first main surface and a secondmain surface and the opposite side surfaces have an inner side surfaceand an outer side surface, the inner side surface of the first quartzcrystal tuning fork tine confronting the inner side surface of thesecond quartz crystal tuning fork tine; and further comprising thesequential steps of forming the quartz crystal tuning fork shape havingthe quartz crystal tuning fork base, and the first and second quartzcrystal tuning fork tines in a first etching process; forming a groovehaving a first side surface opposite the inner side surface and a secondside surface opposite the outer side surface, and a third side surfaceconnecting the first side surface to the second side surface in each ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines in a second etching process differentfrom the first etching process so that the spaced-apart distance betweenthe first and second quartz crystal tuning fork tines is greater than awidth of the groove formed in each of the first and second main surfacesof each of the first and second quartz crystal tuning fork tines;disposing at least one metal film on each of the first and second mainsurfaces and the inner and outer side surfaces of each of the first andsecond quartz crystal tuning fork tines and each of the first and secondside surfaces of the groove formed in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines; disposing a resist on the at least one metal film; forming afirst electrode on each of the first and second side surfaces of thegroove formed in each of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines and a secondelectrode on each of the inner and outer side surfaces of each of thefirst and second quartz crystal tuning fork tines so that the firstelectrode formed on each of the first and second side surfaces of thegroove formed in each of the first and second main surfaces of the firstquartz crystal tuning fork tine is connected to the second electrodeformed on each of the inner and outer side surfaces of the second quartzcrystal tuning fork tine, and the first electrode formed on each of thefirst and second side surfaces of the groove formed in each of the firstand second main surfaces of the second quartz crystal tuning fork tineis connected to the second electrode formed on each of the inner andouter side surfaces of the first quartz crystal tuning fork tine;removing the resist disposed on the at least one metal film; andadjusting an oscillation frequency of the quartz crystal tuning forkresonator.
 21. A method according to claim 18; wherein the opposite mainsurfaces comprise a first main surface and a second main surface and theopposite side surfaces have an inner side surface and an outer sidesurface, the inner side surface of the first quartz crystal tuning forktine confronting the inner side surface of the second quartz crystaltuning fork tine; and further comprising the sequential steps of formingsimultaneously the quartz crystal tuning fork shape having the quartzcrystal tuning fork base, and the first and second quartz crystal tuningfork tines and a plurality of grooves divided in the length direction inat least one of the first and second main surfaces of each of the firstand second quartz crystal tuning fork tines in an etching process sothat the spaced-apart distance between the first and second quartzcrystal tuning fork tines is greater than a width of each of two of thegrooves formed in the at least one of the first and second main surfacesof each of the first and second quartz crystal tuning fork tines;disposing at least one metal film on each of the first and second mainsurfaces and the inner and outer side surfaces of each of the first andsecond quartz crystal tuning fork tines and a surface of each of the twoof the grooves formed in the at least one of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines; disposing a resist on the at least one metal film; forming afirst electrode on the surface of each of the two of the grooves formedin the at least one of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines and a second electrodeon each of the inner and outer side surfaces of each of the first andsecond quartz crystal tuning fork tines so that the first electrodeformed on the surface of each of the two of the grooves formed in the atleast one of the first and second main surfaces of the first quartzcrystal tuning fork tine is connected to the second electrode formed oneach of the inner and outer side surfaces of the second quartz crystaltuning fork tine, and the first electrode formed on the surface of eachof the two of the grooves formed in the at least one of the first andsecond main surfaces of the second quartz crystal tuning fork tine isconnected to the second electrode formed on each of the inner and outerside surfaces of the first quartz crystal tuning fork tine; andadjusting an oscillation frequency of the quartz crystal tuning forkresonator.
 22. A method according to claim 21; wherein the forming stepof the quartz crystal tuning fork shape and the grooves in the etchingprocess includes the step of forming a first groove and a second groovedivided in the length direction in at least one of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines in the etching process so that a width of at least one of thefirst and second grooves formed in the at least one of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines is greater than a distance in the width direction ofthe at least one groove measured from an outer edge of the at least onegroove to an outer edge of the corresponding one of the first and secondquartz crystal tuning fork tines.
 23. A method for manufacturing aquartz crystal oscillator, comprising the steps of: forming a quartzcrystal tuning fork resonator capable of vibrating in a flexural mode ofan inverse phase and having a quartz crystal tuning fork shape, acapacitance ratio r₁ of a fundamental mode of vibration and acapacitance ratio r₂ of a second overtone mode of vibration, the quartzcrystal tuning fork shape having a dimension and a quartz crystal tuningfork base, and first and second quartz crystal tuning fork tinesconnected to the quartz crystal tuning fork base, each of the first andsecond quartz crystal tuning fork tines having opposite main surfacesand opposite side surfaces; forming at least one groove having adimension in at least one of the opposite main surfaces of each of thefirst and second quartz crystal tuning fork tines so that a spaced-apartdistance between the first and second quartz crystal tuning fork tinesis greater than or equal to a width of the at least one groove formed inthe at least one of the opposite main surfaces of each of the first andsecond quartz crystal tuning fork tines; determining the dimension ofeach of the quartz crystal tuning fork shape and the at least one grooveformed in the at least one of the opposite main surfaces of each of thefirst and second quartz crystal tuning fork tines so that thecapacitance ratio r₁ of the fundamental mode of vibration of the quartzcrystal tuning fork resonator is less than the capacitance ratio r₂ ofthe second overtone mode of vibration thereof; providing a case having amounting portion and a lid for covering an open end of the case;mounting the quartz crystal tuning fork resonator on the mountingportion of the case; connecting the lid to the case to cover the openend of the case; providing an amplifier, a plurality of capacitors andat least one resistor; and electrically connecting the quartz crystaltuning fork resonator to the amplifier, the capacitors and the at leastone resistor to form a quartz crystal oscillating circuit.
 24. A methodaccording to claim 23; wherein the quartz crystal tuning fork resonatorhas a merit value M₁ of the fundamental mode of vibration and a meritvalue M₂ of the second overtone mode of vibration, the merit value M₁being defined by the ratio (Q₁/r₁) and the merit value M₂ being definedby the ratio (Q₂/r₂), where Q₁ and Q₂ represent a quality factor of thefundamental mode of vibration and the second overtone mode of vibration,respectively, of the quartz crystal tuning fork resonator and r₁ and r₂represent the capacitance ratio of the fundamental mode of vibration andthe second overtone mode of vibration, respectively, of the quartzcrystal tuning fork resonator; wherein the opposite main surfaces have afirst main surface and a second main surface; and further comprising thesteps of forming a groove having a dimension in each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines; forming an electrode on a surface of the grooveformed in each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines so that the electrodeformed on the surface of the groove formed in each of the first andsecond main surfaces of the first quartz crystal tuning fork tine has anelectrical polarity opposite to an electrical polarity of the electrodeformed on the surface of the groove formed in each of the first andsecond main surfaces of the second quartz crystal tuning fork tine; anddetermining the dimension of each of the quartz crystal tuning forkshape and the groove formed in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines so that the merit value M₁ of the fundamental mode of vibration ofthe quartz crystal tuning fork resonator is greater than 65 and themerit value M₂ of the second overtone mode of vibration thereof is lessthan
 30. 25. A method according to claim 23; wherein the opposite mainsurfaces have a first main surface and a second main surface; whereinthe forming step of the at least one groove includes the step of forminga groove having a dimension in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines so that the spaced-apart distance between the first and secondquartz crystal tuning fork tines is greater than or equal to a width ofthe groove formed in each of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines; and furthercomprising the step of forming an electrode having a dimension on asurface of the groove formed in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines so that the electrode formed on the surface of the groove formedin each of the first and second main surfaces of the first quartzcrystal tuning fork tine has an electrical polarity opposite to anelectrical polarity of the electrode formed on the surface of the grooveformed in each of the first and second main surfaces of the secondquartz crystal tuning fork tine; wherein the determining step includesthe step of determining the dimension of each of the quartz crystaltuning fork shape, the groove formed in each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines and the electrode formed on the surface of the groove formed ineach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that the capacitance ratio r₁of the fundamental mode of vibration of the quartz crystal tuning forkresonator is less than the capacitance ratio r₂ of the second overtonemode of vibration thereof and the capacitance ratio r₂ is greater than1500; and further comprising the step of arranging the quartz crystaloscillating circuit in an electronic apparatus having a display portion;wherein an output signal of the quartz crystal oscillating circuit is aclock signal for use in operation of the electronic apparatus to displaytime information at the display portion, the clock signal having anoscillation frequency of the fundamental mode of vibration of the quartzcrystal tuning fork resonator and the oscillation frequency of thefundamental mode of vibration thereof being about 32.768 kHz with afrequency deviation within a range of −100 ppm to +100 ppm.
 26. A methodaccording to claim 23; wherein the opposite main surfaces have a firstmain surface and a second main surface; wherein the forming step of thequartz crystal tuning fork resonator includes the step of forming thequartz crystal tuning fork base having a length l₂ less than 0.5 mm; andwherein the forming step of the at least one groove includes the step offorming the at least one groove in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines so that a distance in the width direction of the at least onegroove measured from an outer edge of the at least one groove to anouter edge of the corresponding one of the first and second quartzcrystal tuning fork tines is less than 0.015 mm.
 27. A method accordingto claim 23; wherein the opposite main surfaces have a first mainsurface and a second main surface and the opposite side surfaces have afirst side surface and a second side surface; wherein the case has athrough-hole; wherein the forming step of the at least one grooveincludes the step of forming the at least one groove in each of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines so that the spaced-apart distance between thefirst and second quartz crystal tuning fork tines is greater than awidth of the at least one groove formed in each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines; and further comprising the sequential steps of forming the quartzcrystal tuning fork shape having the quartz crystal tuning fork base,and the first and second quartz crystal tuning fork tines in a firstetching process; forming the at least one groove in each of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines in a second etching process different from the firstetching process so that the spaced-apart distance between the first andsecond quartz crystal tuning fork tines is greater than the width of theat least one groove formed in each of the first and second main surfacesof each of the first and second quartz crystal tuning fork tines;disposing at least one metal film on each of the first and second mainsurfaces and the first and second side surfaces of each of the first andsecond quartz crystal tuning fork tines and a surface of the at leastone groove formed in each of the first and second main surfaces of eachof the first and second quartz crystal tuning fork tines; disposing aresist on the at least one metal film; forming a first electrode on thesurface of the at least one groove formed in each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines and a second electrode on each of the first and secondside surfaces of each of the first and second quartz crystal tuning forktines so that the first electrode has an electrical polarity opposite toan electrical polarity of the second electrode; removing the resistdisposed on the at least one metal film; mounting the quartz crystaltuning fork resonator on the mounting portion of the case; adjusting anoscillation frequency of the quartz crystal tuning fork resonator;connecting the lid to the case to cover the open end thereof; anddisposing a metal or a glass into the through-hole of the case to closethe through-hole thereof in a vacuum after the connecting step of thelid and the case.
 28. A method according to claim 27; further comprisingthe step of arranging the quartz crystal oscillating circuit in anelectronic apparatus having a display portion; wherein an output signalof the quartz crystal oscillating circuit is a clock signal for use inoperation of the electronic apparatus to display time information at thedisplay portion, the clock signal having an oscillation frequency of thefundamental mode of vibration of the quartz crystal tuning forkresonator and the oscillation frequency of the fundamental mode ofvibration thereof being about 32.768 kHz with a frequency deviationwithin a range of −100 ppm to +100 ppm.
 29. A method according to claim27; further comprising the step of adjusting the oscillation frequencyof the quartz crystal tuning fork resonator after the disposing step ofthe metal or the glass so that the oscillation frequency thereof isabout 32.768 kHz with a frequency deviation within a range of −50 ppm to+50 ppm.
 30. A method according to claim 23; wherein the opposite mainsurfaces have a first main surface and a second main surface; andwherein the forming step of the at least one groove includes the step offorming a plurality of grooves having a first groove and a second groovein each of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that a width of at least oneof the first and second grooves formed in each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines is within a range of 0.03 mm to 0.12 mm.
 31. A method according toclaim 23; wherein the opposite main surfaces have a first main surfaceand a second main surface; wherein the forming step of the at least onegroove includes the step of forming a plurality of grooves having afirst groove and a second groove in each of the first and second mainsurfaces of each of the first and second quartz crystal tuning forktines so that a width of at least one of the first and second groovesformed in each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines is greater than orequal to a distance in the width direction of the at least one groovemeasured from an outer edge of the at least one groove to an outer edgeof the corresponding one of the first and second quartz crystal tuningfork tines; and wherein the quartz crystal tuning fork shape having thequartz crystal tuning fork base, and the first and second quartz crystaltuning fork tines is formed simultaneously with the grooves having thefirst and second grooves.
 32. A method according to claim 23; whereinthe opposite main surfaces have a first main surface and a second mainsurface; wherein the forming step of the at least one groove includesthe step of forming the at least one groove in each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines so that the spaced-apart distance between the firstand second quartz crystal tuning fork tines is greater than or equal toa width of the at least one groove formed in each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines and is within a range of 0.05 mm to 0.35 mm, and alength of the at least one groove formed in each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines is within a range of 0.35 mm to 1.15 mm; wherein the quartzcrystal tuning fork shape having the quartz crystal tuning fork base,and the first and second quartz crystal tuning fork tines is formedsimultaneously with the at least one groove formed in each of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines; and further comprising the step of arranging thequartz crystal oscillating circuit in an electronic apparatus having adisplay portion; wherein an output signal of the quartz crystaloscillating circuit is a clock signal for use in operation of theelectronic apparatus to display time information at the display portion,the clock signal having an oscillation frequency of the fundamental modeof vibration of the quartz crystal tuning fork resonator and theoscillation frequency of the fundamental mode of vibration thereof beingabout 32.768 kHz with a frequency deviation within a range of −100 ppmto +100 ppm.
 33. A method according to claim 23; wherein the oppositemain surfaces have a first main surface and a second main surface, eachof the first and second main surfaces of each of the first and secondquartz crystal tuning fork tines having a central linear portion;wherein the forming step of the at least one groove includes the step offorming the at least one groove in the central linear portion of each ofthe first and second main surfaces of each of the first and secondquartz crystal tuning fork tines so that the spaced-apart distancebetween the first and second quartz crystal tuning fork tines is greaterthan or equal to a width of the at least one groove formed in thecentral linear portion of each of the first and second main surfaces ofeach of the first and second quartz crystal tuning fork tines; wherein alength of the at least one groove formed in the central linear portionof each of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines and cut into a main surface ofthe quartz crystal tuning fork base is defined by l₁and a length of theat least one groove cut into the main surface of the quartz crystaltuning fork base is defined by l₃; wherein a length of the at least onegroove formed in the central linear portion of each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines is defined by l₁-l₃; wherein the at least one grooveis formed in the central linear portion of each of the first and secondmain surfaces of each of the first and second quartz crystal tuning forktines so that the length l₃ is substantially zero; and wherein thequartz crystal tuning fork shape having the quartz crystal tuning forkbase, and the first and second quartz crystal tuning fork tines isformed before the at least one groove is formed in the central linearportion of each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines so that the length l₃is substantially zero.
 34. A method according to claim 23; wherein theopposite main surfaces have a first main surface and a second mainsurface; wherein the forming step of the at least one groove includesthe step of forming the at least one groove in each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines so that the spaced-apart distance between the firstand second quartz crystal tuning fork tines is greater than or equal toa width of the at least one groove formed in each of the first andsecond main surfaces of each of the first and second quartz crystaltuning fork tines; wherein a length of the at least one groove formed ineach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines and cut into a main surface ofthe quartz crystal tuning fork base is defined by l₁ and a length of theat least one groove cut into the main surface of the quartz crystaltuning fork base is defined by l₃; wherein a length of the at least onegroove formed in each of the first and second main surfaces of each ofthe first and second quartz crystal tuning fork tines is defined byl₁-l₃; wherein the at least one groove is formed in each of the firstand second main surfaces of each of the first and second quartz crystaltuning fork tines so that the length l₃ is substantially zero; andwherein the quartz crystal tuning fork shape having the quartz crystaltuning fork base, and the first and second quartz crystal tuning forktines is formed simultaneously with the at least one groove formed ineach of the first and second main surfaces of each of the first andsecond quartz crystal tuning fork tines so that the length l₃ issubstantially zero.
 35. A method according to claim 23; wherein theopposite main surfaces have a first main surface and a second mainsurface, each of the first and second main surfaces of each of the firstand second quartz crystal tuning fork tines having a central linearportion; wherein the forming step of the at least one groove includesthe step of forming the at least one groove in the central linearportion of each of the first and second main surfaces of each of thefirst and second quartz crystal tuning fork tines so that thespaced-apart distance between the first and second quartz crystal tuningfork tines is within a range of 0.05 mm to 0.35 mm and a length of theat least one groove formed in the central linear portion of each of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines is within a range of 0.35 mm to 1.15 mm;wherein the step of forming the quartz crystal tuning fork shape havingthe quartz crystal tuning fork base, and the first and second quartzcrystal tuning fork tines is performed before the step of forming the atleast one groove formed in the central linear portion of each of thefirst and second main surfaces of each of the first and second quartzcrystal tuning fork tines; and further comprising the step of arrangingthe quartz crystal oscillating circuit in an electronic apparatus havinga display portion; wherein an output signal of the quartz crystaloscillating circuit is a clock signal for use in operation of theelectronic apparatus to display time information at the display portion,the clock signal having an oscillation frequency of the fundamental modeof vibration of the quartz crystal tuning fork resonator and theoscillation frequency of the fundamental mode of vibration thereof beingabout 32.768 kHz with a frequency deviation within a range of −100 ppmto +100 ppm.